Admittedly, the quantum correlation quantification in qudit-qudit systems (\(d_{1}\otimes d_{2}\) ) remains an open problem. In this sense, a glimmer of hope comes from the Ref.[1]}, in which the authors emphasize that the closed form of the local quantum uncertainty can be obtained for quantum states of dimension \(d_{1}\otimes d_{2}\) , by using the generators of the algebra \(SU\left(d_{1}\right)\)  in optimization as a special unitary group. The explicit expression of the local quantum uncertainty in this case becomes
\({\cal U}_{A}\left(\rho \right)=\frac{2}{d_{1}}-\xi _{\max }\left(\hat{\cal W}\right),\) 
